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Modelling cell generation times by using the tempered stable distribution


  • Karen J. Palmer
  • Martin S. Ridout
  • Byron J. T. Morgan


We show that the family of tempered stable distributions has considerable potential for modelling cell generation time data. Several real examples illustrate how these distributions can improve on currently assumed models, including the gamma and inverse Gaussian distributions which arise as special cases. Our applications concentrate on the generation times of oligodendrocyte progenitor cells and the yeast "Saccharomyces cerevisiae". Numerical inversion of the Laplace transform of the probability density function provides fast and accurate approximations to the tempered stable density, for which no closed form generally exists. We also show how the asymptotic population growth rate is easily calculated under a tempered stable model. Copyright (c) 2008 Royal Statistical Society.

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  • Karen J. Palmer & Martin S. Ridout & Byron J. T. Morgan, 2008. "Modelling cell generation times by using the tempered stable distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 379-397.
  • Handle: RePEc:bla:jorssc:v:57:y:2008:i:4:p:379-397

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    References listed on IDEAS

    1. D. J. Cole & M. S. Ridout & B. J. T. Morgan & L. J. Byrne & M. F. Tuite, 2007. "Approximations for Expected Generation Number," Biometrics, The International Biometric Society, vol. 63(4), pages 1023-1030, December.
    2. M. S. Ridout & D. J. Cole & B. J. T. Morgan & L. J. Byrne & M. F. Tuite, 2006. "New Approximations to the Malthusian Parameter," Biometrics, The International Biometric Society, vol. 62(4), pages 1216-1223, December.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Normal modified stable processes," Economics Papers 2001-W6, Economics Group, Nuffield College, University of Oxford.
    4. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    5. Gagan L. Choudhury & Ward Whitt, 1997. "Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms," INFORMS Journal on Computing, INFORMS, vol. 9(2), pages 175-184, May.
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    Cited by:

    1. Imai, Junichi & Kawai, Reiichiro, 2011. "On finite truncation of infinite shot noise series representation of tempered stable laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4411-4425.
    2. Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
    3. Michael Grabchak, 2016. "On the consistency of the MLE for Ornstein–Uhlenbeck and other selfdecomposable processes," Statistical Inference for Stochastic Processes, Springer, vol. 19(1), pages 29-50, April.

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